Oscillations of a drop in aerodynamic levitation

The aim of this work is to model the axisymmetric small-amplitude oscillation modes of a liquid drop in aerodynamic levitation over a horizontal porous wall. In this objective, the boundary element method (BEM) was chosen to solve numerically the unsteady Stokes equations in the frequency domain. Arguments are presented to justify this choice. The use of this numerical method is quite original to describe coupled flows, such as those characterizing the levitation problem. A numerical tool, based on the BEM, was developed to perform the normal-mode analysis for the axisymmetric oscillations. The set of unsteady Stokes equations and boundary conditions governing the behavior of the fluids in both internal and external domains led to a linear homogeneous system with pulsation as a parameter. The eigenvalues of this system give the frequencies, while the associated eigenvectors provide the shapes of the oscillation modes. A sensitivity analysis was performed to choose the optimal values of the numerical parameters. Furthermore, the study of the influence of the physical parameters revealed the consistency of the modelization. At last, a comparison with experimental results proved to be satisfactory.